This column will change your life: What's the worst that could happen?

You were as relieved as me, I'm sure, to learn that the terrifying Mayan prophecy about the world ending in 2012 has been postponed, thanks to an apparent error in converting the Mayan calendar. (You've got to feel sorry for the authors of those "2012 apocalypse" cash-in books, though, haven't you? Oh, wait, no, you haven't.) But my relief reverted to terror when I opened The Watchman's Rattle, a book by the biologist and business guru Rebecca Costa that's subtitled Thinking Our Way Out of Extinction. The Mayans, she argues, do indeed have an alarming message for us, as to why our efforts to solve problems – societal and personal – so often go wrong. Unlike the 2012 predictions, her thesis doesn't involve celestial bodies crashing into the earth, which is a point in its favour, unless you're the asteroid-fixated former MP Lembit Opik. But you're probably not, and in any case, Costa's argument is perfectly troubling enough.

Nobody agrees why the Mayans' astonishingly advanced civilisation suddenly collapsed between 750 and 850. Theories abound – drought, disease, war – but Costa suggests it was all of the above. The Mayans had reached their "cognitive threshold", creating a society so complex that it outstripped their brains' capacity to understand it; they could no longer think their way out of their problems. You needn't share all the controversial positions of Costa's specialism, sociobiology, to see how we might be in the same boat today, only worse. Our evolved cognitive capacity is much the same as in 850, but society is vastly more complex: "The rate at which the human brain can evolve new faculties," Costa writes, "is millions of years slower than the rate at which humans generate change and produce new information." What's the solution to global warming, financial crises, terrorism? The answer may be beyond us.

This matters on a personal level, too, and not solely because the destruction of civilisation would be somewhat dispiriting. The complexity of even far more mundane challenges – how to stay healthy, how to be happy in relationships or work – can feel equally defeating, whether or not they're technically beyond our abilities. Any given solution won't work, by definition: Costa defines complexity as when "there are many more wrong solutions than right ones". Worse, they lull us into thinking we're tackling the matter, so extinguishing the sense of urgency. (Are you eschewing plastic bags, imagining you're "doing your bit" for the planet?) The only rational tactic may be trying everything at once – what Costa calls "parallel incrementalism" – in full knowledge that most methods will fail. Should we be fighting climate change at the level of politics, lifestyle or technology? Should you be addressing your chronic lack of energy by sleeping more, eating better or seeing a doctor? All of the above.

We need to think, Costa says, like venture capitalists, who make a fortune despite 80% of the businesses they invest in failing; they know that 20% won't, but not which ones. For complex problems, trying one solution and getting upset when it fails is preposterous: any single solution is likely to fail. The mindset we need isn't the positive-thinking mantra that failure is impossible; it's that failures are inevitable, and for good reason. It's an unexpectedly hopeful conclusion: we may never really understand how to get what we want, or stave off the very worst – yet we may manage it anyway.